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Short Eigenvectors and Multidimensional Theta Functions

Summary: Short Eigenvectors and
Multidimensional Theta Functions
Ron M. Adin \Lambda
Department of Mathematics and Computer Science
Bar­Ilan University
Ramat­Gan 52900, ISRAEL
E­mail: radin@bimacs.cs.biu.ac.il
Yaacov Kopeliovich y
Department of Mathematics
University of California
Irvine, CA 92717
E­mail: ykopelio@math.uci.edu
Version of December 19, 1995
A certain family of symmetric matrices, with entries \Sigma1, is known to determine
all the quartic relations that hold between multi­dimensional theta constants.
Attention is drawn here to combinatorial properties of the shortest possible
quartic relations, corresponding to vectors with minimal support in a certain
eigenspace of such a matrix. A lower bound for the size of the support is estab­
lished, exhibiting a ``phase transition'' at dimension four. The multiplicity­free


Source: Adin, Ron - Department of Mathematics, Bar Ilan University


Collections: Mathematics